Average Error: 47.6 → 14.7
Time: 14.4s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double i, double n) {
	return ((double) (100.0 * ((double) (((double) (((double) pow(((double) (1.0 + ((double) (i / n)))), n)) - 1.0)) / ((double) (i / n))))));
}

↓
double code(double i, double n) {
	double VAR;
	if ((i <= -9.043975738872494e-10)) {
		VAR = ((double) (100.0 * ((double) (n * ((double) (((double) (((double) pow(((double) (i / n)), n)) - 1.0)) / i))))));
	} else {
		double VAR_1;
		if ((i <= 0.04307656589136779)) {
			VAR_1 = ((double) (100.0 * ((double) (((double) (((double) (((double) cbrt(((double) (((double) (i * 1.0)) + ((double) (((double) (n * ((double) log(1.0)))) + ((double) (((double) (i * i)) * ((double) (0.5 - ((double) (((double) log(1.0)) * 0.5)))))))))))) / ((double) cbrt(i)))) * ((double) (((double) cbrt(((double) (((double) (i * 1.0)) + ((double) (((double) (n * ((double) log(1.0)))) + ((double) (((double) (i * i)) * ((double) (0.5 - ((double) (((double) log(1.0)) * 0.5)))))))))))) / ((double) cbrt(i)))))) * ((double) (n * ((double) (((double) cbrt(((double) (((double) (i * 1.0)) + ((double) (((double) (n * ((double) log(1.0)))) + ((double) (((double) (i * i)) * ((double) (0.5 - ((double) (((double) log(1.0)) * 0.5)))))))))))) / ((double) cbrt(i))))))))));
		} else {
			double VAR_2;
			if ((i <= 6.213782009528768e+209)) {
				VAR_2 = ((double) (100.0 * ((double) (((double) (((double) (((double) pow(((double) (((double) (i / n)) + 1.0)), ((double) (n * 2.0)))) - ((double) (1.0 * 1.0)))) / ((double) (1.0 + ((double) pow(((double) (((double) (i / n)) + 1.0)), n)))))) / ((double) (i / n))))));
			} else {
				VAR_2 = ((double) (100.0 * ((double) (((double) (((double) (1.0 + ((double) (((double) (i * 1.0)) + ((double) (n * ((double) log(1.0)))))))) - 1.0)) / ((double) (i / n))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus i
Bits error versus n
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original47.6
Target47.5
Herbie14.7
\[\]
Derivation
  1. Split input into 4 regimes
  2. if  i  < -9.04397573887249397e-10
    1. Initial program 28.5
      \[\]
    2. Taylor expanded around inf 64.0
      \[\leadsto \]
    3. Simplified19.7
      \[\leadsto \]
    if -9.04397573887249397e-10 <  i  < 0.0430765658913677893
    1. Initial program 58.2
      \[\]
    2. Taylor expanded around 0 25.9
      \[\leadsto \]
    3. Simplified25.9
      \[\leadsto \]
    4. Using strategy rm
    5. Applied *-un-lft-identity25.9
      \[\leadsto \]
    6. Applied add-cube-cbrt26.7
      \[\leadsto \]
    7. Applied times-frac26.7
      \[\leadsto \]
    8. Applied add-cube-cbrt26.1
      \[\leadsto \]
    9. Applied times-frac13.8
      \[\leadsto \]
    10. Simplified13.8
      \[\leadsto \]
    11. Simplified9.3
      \[\leadsto \]
    if 0.0430765658913677893 <  i  < 6.2137820095287683e209
    1. Initial program 30.1
      \[\]
    2. Using strategy rm
    3. Applied flip--30.1
      \[\leadsto \]
    4. Simplified30.0
      \[\leadsto \]
    5. Simplified30.0
      \[\leadsto \]
    if 6.2137820095287683e209 <  i 
    1. Initial program 32.6
      \[\]
    2. Taylor expanded around 0 33.7
      \[\leadsto \]
    3. Simplified33.7
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification14.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (i n)
  :name "Compound Interest"
  :precision binary64

  :herbie-target
  (* 100.0 (/ (- (exp (* n (if (== (+ 1.0 (/ i n)) 1.0) (/ i n) (/ (* (/ i n) (log (+ 1.0 (/ i n)))) (- (+ (/ i n) 1.0) 1.0))))) 1.0) (/ i n)))

  (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))